Mrs May says in her letter the Commons defeat, in which dozens of Conservatives abstained, was “disappointing”.

“I do not underestimate how deeply or how sincerely colleagues hold the views which they do on this important issue – or that we are all motivated by a common desire to do what is best for our country, even if we disagree on the means of doing so,” she writes.

“But I believe that a failure to make the compromises necessary to reach and take through Parliament a withdrawal agreement which delivers on the result of the referendum will let down the people who sent us to represent them and risk the bright future that they all deserve.”

Mrs May says without a withdrawal deal passing in the Commons, Parliament might stop Brexit altogether.

Alternatively, she says the UK might leave without a deal, which would disrupt the economy and damage jobs.

But BBC political correspondent Ben Wright said Mrs May’s letter showed “no hint of a change in tactic” for ending the stalemate.

Campaigners for another referendum on Brexit have said there will be a major protest the weekend before Britain’s scheduled departure date on 29 March.